GCSE Maths (AQA)

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Combined Graph Translations

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Algebra Graphs

Combined Graph Translations

7:53 Graph Translations
Spec A13
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  • Adding a constant to both the input and output of a function will cause the graph to move horizontally and vertically.
  • Adding a constant to the input of a function will move the graph to the left.
  • Adding a constant to the output of a function will move the graph up.
  • The graph of the function f(x + a + b) is the graph of the function f(x) translated by the vector (-a, b).
  • The top number of the translation vector represents horizontal movement (negative for left, positive for right).
  • The bottom number of the translation vector represents vertical movement (negative for down, positive for up).
  • The equation of a translated graph can be found by adding/subtracting the translation values to the original equation.
  • To find the translation vector, identify an equivalent point on both graphs and determine the horizontal and vertical movements.
  • The equation of the translated graph is f(x - a + b).

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